State in brief the distribution of terms in A, E, I, O propositions.
Answers
Explanation:
There are four types of propositions, namely (i) Universal affirmative (or A-proposition) (ii) Universal negative (or E-proposition), (iii) Particular affirmative (or I-proposition) and (iv) Particular negative (or O-proposition).
Only these types of propositions can occur in any logical argument. Of course, each proposition, in addition to quantifier and copula, must have a subject term and a predicate term. Now we wish to explain a crucial notion viz. ‘distribution of terms’ in a logical proposition, which plays an important role in developing rules for deductive arguments.
In categorical proposition, terms designate classes of objects. In other words, the subject and predicate terms in a categorical proposition designate classes of objects, and the categorical proposition may be regarded as about these classes.
For example, the proposition “All men are mortal” is about the class of men and the class of mortal beings. More over, it is about all men since we are talking about all the members of the class designated by the term, ‘men’. On the other hand, in asserting the proposition “All men are mortal”, we are not asserting or talking about all the members of the class designated by the predicate term ‘mortal’.
Hence, only a pan of the class of objects designated by the term ‘mortal’ is being considered. So, in any categorical proposition we may refer to either all or some members of a class designated by a term. To express this insight, Aristotle introduces a technical term called ‘distribution’.
A term is said to be distributed in a proposition if and only if it refers to the whole of the class designated by the term. Otherwise, the term is called undistributed. If a term refers to a part of the class designated by the term, it is called undistributed. Alternatively, we may say that if a term refers to the entire denotation of a term (or refers to all the members’ of the class designated by the term) either affirmatively or negatively, then the term in question is distributed. On the other hand, if only a part of a denotation is being referred to by the term then it is called undistributed.
Let us examine which term is distributed in which type of proposition. As we know, there are four types of categorical proposition namely A, E, I and O-propositions. For convenience, let us state the logical form or the structure along with a concrete example of each of the four types of proposition in a tabular form.
